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NASA NTRS2020

Modeling Heatshield Erosion Due to Dust Particle Impacts for Martian Entries

Heatshield design for spacecraft entering the atmosphere of Mars may be affected by the presence of atmospheric dust. Particle impacts with sufficient kinetic energy can cause spallation damage to the heatshield that must be estimated. The dust environment in terms of particle size distribution and number density can be inferred from ground-based or atmospheric observations at Mars. Using a Lagrangian approach, the particle trajectories through the shock layer can be computed using a set of coupled ordinary differential equations. The dust particles are small enough that non-continuum effects must be accounted for when computing the drag coefficient and heat transfer to the particle surface. Surface damage correlations for impact crater diameter and penetration depth are presented for fused-silica, AVCOAT, Shuttle tiles, cork, and Norcoat Liège. The cork and Norcoat Liège correlations are new and were developed in this study. The modeling equations presented in this paper are applied to compute the heatshield erosion due to dust particle impacts on the ExoMars Schiaparelli entry capsule during dust storm conditions.

Palmer, Grant↗
NASA NTRSDate not supplied

Simulation of Dust-Laden Flow in the DLR L2K Facility

An integrated CFD-particle trajectory code called US3D-DUST is used to simulate the dusty flow environments performed in the German Aerospace Center (DLR) L2K arcjet facility. The particle trajectory code uses a Lagrangian approach, where the particle trajectories through the shock layer can be computed using a set of coupled ordinary differential equations. The L2K experiments measured mass loss to flat-face shaped samples of the Norcoat-Liège thermal protection system material. The US3D-DUST simulations were able to reproduce particle velocity and stagnation point heating rate data. When applied to the L2K dusty flow conditions, the US3D-DUST predictions of mass loss due to particle impacts and surface recession rates over-predicted the experimental values. It is recommended to perform additional dusty flow tests in the L2Kto provide and improve the surface damage model for Norcoat-Liège.

Thermal protection systems↗
NASA NTRS2022

An ODE-Fitting Approach to Estimate Critical Aircraft Performance Parameters for Trajectory Prediction

Ground-based decision support tools (DST) in air traffic management (ATM) typically perform trajectory prediction based on aircraft performance model (APM) parameters, but some or all of these parameters might not be readily available. In particular, the three critical parameters required for trajectory prediction are the thrust setting, drag coefficients, and takeoff weight of the aircraft. Unfortunately, these parameters are coupled and appear together in physics-based kinetic models. Past approaches utilize data from a specific phase of flight (climb, level flight or descent), where one or more of the parameters are assumed to be known and estimate the remaining unknown parameters. This approach introduces bias/errors and also does not extend to scenarios where all of the above parameters are not known with sufficient accuracy. This paper is the first of its kind to propose a generalized framework for simultaneous estimation of all three critical APM parameters (thrust, drag, and mass). The proposed approach utilizes data from both the climb and descent phases and fits the ordinary differential equation for altitude in each phase using historical trajectory data available from radar tracks or ADS-B. The approach yields a set of optimized APM parameters that are best suited to fit each historical flight record. The methodology is applied on on sample flights from three different aircraft types, and the results demonstrate low fit error and consequently will yield a high level of prediction accuracy.

trajectory prediction, aircraft performance model,↗
NASA NTRSDate not supplied

Flow field Reconstruction for Inhomogeneous Turbulence using Data and Physics Driven Models

A methodology combining Large Eddy Simulation (LES) trained data and a physics driven wave packet model to obtain a reduced order reconstruction for broadband, three-dimensional, temporally stationary but spatially inhomogeneous, incompressible turbulence. Wake turbulence generated by an axisymmetric dragging disk with a turbulent co-flow serves as the benchmark test case. We begin by studying the proper-orthogonal decomposition of the turbulent fluctuations taken from a high-resolution LES to first identify whether the fields demonstrate a low-rank character. It is argued that the presence of the turbulent co-flow results in a largely broadband character lacking any tonal properties. This is especially true for Strouhal numbers greater than 1 and only a small fraction of energy is contained in the leading order Kelvin-Helmholtz modes. As such reconstructions and reduced order modeling purely relying on data from LES does not appear to be a lucrative solution - contrary to problems with strongly tonal character. To supplement the missing energy from a low order truncated mode expansion, we utilize a physics based super-resolution (enrichment) algorithm that relies on spatio-temporally localized Gabor wave packets whose time evolution is described using a set of ordinary differential equations. The reconstructed flow has single- and two-point correlations that are consistent with the reference high resolution simulation data.

SLS↗
NASA NTRSDate not supplied

Machine Learning based Aircraft Performance Model Estimation for Trajectory Prediction

The accurate prediction of aircraft trajectory by ground-based decision support tools is a critical component of air traffic management in the US National Airspace System (NAS). Accurate predictions of where the aircraft will be in the future or when they will arrive at specific locations (e.g., fixes) is a key enabler for sequencing and efficient arrival management of flights. Traditional physics based aircraft trajectory prediction relies on a simplified point-mass total energy model whose parameters are referred to as Aircraft Performance Model (APM) parameters. Even though the performance coefficients and weight of an aircraft are a vital part of the aircraft performance model’s predictions and accuracy, these coefficients are proprietary in nature and therefore, unavailable to decision-support tools. Current approaches freeze some coefficients to default base of aircraft data (BADA) values and optimize others. However, the APM parameters are highly coupled by the flight dynamics and prioritizing one parameter over others leads to bias and skewed predictions. To alleviate this problem, we provide a combined optimization framework to predict all the critical (thrust, drag and weight) APM parameters. This paper is focused on training Machine Learning (ML) models that map historical flights to optimized APM parameters that provide the best fit (in terms of prediction error). Our dataset obtained from NASA’s Sherlock data warehouse is comprised of thousands of historical flights and includes weather and track data collected from 2019. Using different subsets of relevant features (e.g., aircraft type), we trained several ML models to estimate the aircraft’s take off weight, drag polar coefficients (both parasitic and lift induced), and thrust settings (multiplier applied to the maximum engine thrust). The chosen flights are from three of the most common aircraft types (B738, B737, and A320) arriving at four airports (LAX, DEN, MSP, and DFW). Our ML approach is comprised of two different solutions: 1- using a subset of features that are known prior to the flight departure and do not change during flight (such as engine type, current temperature at departure & destination airports, aircraft type) and 2 - using a subset of temporal features of the flight trajectory (such as cruise altitude, Mach, airspeed, and rate of climb) in addition to the pre-departure features from the first solution. The labels or target variables are the APM parameters that were obtained by an optimized ordinary differential equations (ODE) fitting process (applied to individual flights). The ODE-fitting is very time intensive and is therefore performed offline. Thus, training an ML model to learn the relationship between the flight features and ODE-generated labels enables faster estimation of the APM parameters and is therefore amenable to real-time prediction. Various ML models including linear regression, random forest, XGBoost, and neural network were trained, and the results are compared. After model validation and hyperparameter-tuning, we observed that the Random Forest model outperformed the other three models by the overall mean square error (MSE) of 2% for the first solution and 1.5% for the second solution. Finally, the ML-derived parameters are compared against default BADA APM parameters using NASA’s Autonomy Development toolkit (ADK) simulation software. The simulation results for one of each aircraft type is shown and discussed.

Aida Sharif Rohani↗
NASA NTRSDate not supplied

Machine Learning Approach for Aircraft Performance Model Parameter Estimation for Trajectory Prediction Applications

Inaccurate prediction of aircraft trajectory by ground-based decision support tools (DST) is a major concern in air traffic management (ATM). Aircraft trajectory prediction tools rely on a simplified point-mass aircraft performance model (APM) to make their predictions. Even though the performance coefficients and weight of an aircraft are a vital part of the APM’s predictions and accuracy, these coefficients are proprietary in nature and therefore, unavailable to DSTs. Current ATM research focuses on improving the estimate of some APM parameters by freezing all other coefficients. This simplified approach introduces unwanted sources of bias and negatively impacts the accuracy of the performance model. In this paper, we apply machine learning (ML) techniques for the simultaneous prediction of three key APM parameters (two drag coefficients and the initial aircraft weight). To accomplish this, we employ an ordinary differential equation (ODE) fitting approach to generate optimized APM parameter labels customized to each individual flight record. Subsequently, we train ML models to capture the relationship between the historical data and the optimized APM parameters. Two different ML model solutions are applied and APM coefficients are predicted for unseen flights. The results indicate that the ML models are able to capture the relationship between APM parameters and flight-related features with good accuracy.

trajectory prediction, machine learning, aircraft ↗
NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗
NASA NTRSDate not supplied

Obtaining Accurate Derivatives Across Adaptive-Step Integration

Obtaining derivatives through the integration of a set of ordinary differential equations is of interest to a number of fields of research. Approaches for doing so that are available in the literature, however, do not account for details associated with variable step integrator that cause inaccuracies in the total derivatives. In this paper, we explore the causes of the accumulation of derivative error in adaptive-step Runge-Kutta integration schemes and propose a solution to eliminate them. The new algorithm proposed is a transformation of each step of a Runge-Kutta integration into a set of residual equations. This work demonstrates the improvement in accuracy of total derivatives when the new algorithm is utilized.

Kaushik Ponnapalli↗
NASA NTRS2024

Accelerating Continuous Variable Coherent Ising Machines Via Momentum

The Coherent Ising Machine (CIM) is a non-conventional architecture that takes inspiration from physical annealing processes to solve Ising problems heuristically. Its dynamics are naturally continuous and described by a set of ordinary differential equations that have been proven to be useful for the optimization of continuous variables nonconvex quadratic optimization problems. The dynamics of such Continuous Variable CIMs (CV-CIM) encourage optimization via optical pulses whose amplitudes are determined by the negative gradient of the objective; however, standard gradient descent is known to be trapped by local minima and hampered by poor problem conditioning. In this work, we propose to modify the CV-CIM dynamics using more sophisticated pulse injections based on tried-and-true optimization techniques such as momentum and Adam. Through numerical experiments, we show that the momentum and Adam updates can significantly speed up the CV-CIM’s convergence and improve sample diversity over the original CV-CIM dynamics. We also find that the Adam-CV-CIM’s performance is more stable as a function of feedback strength, especially on poorly conditioned instances, resulting in an algorithm that is more robust, reliable, and easily tunable. More broadly, we identify the CIM dynamical framework as a fertile opportunity for exploring the intersection of classical optimization and modern analog computing.

Ising Model↗
NASA NTRSDate not supplied

Robust Trajectory Optimization Techniques Using a Sweeping Gradient Method and Linear Covariance Analysis

We present robust trajectory optimization techniques using a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov). SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve robust optimal trajectory design problems. We describe the individual methods and some details on how they can be combined. Then we apply the combined techniques to a variety of orbital trajectory design problems to demonstrate its use, including minimum fuel transfer and mid-course correction burn scheduling.

Benjamin W L Margolis↗
NASA NTRSDate not supplied

Co-Optimization of Navigation System Requirements and Trajectory Design Using a Sweeping Gradient Method and Linear Covariance Analysis

We describe the application of a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov) to the co-optimization of navigation system requirement generation and robust trajectory design. SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve a combined robust optimal trajectory and navigation system design problem. In this paper, we formulate the required models to apply the combined SGM and LinCov techniques to a Near-Rectilinear Halo Orbit rendezvous approach scenario and show results for several intermediate problems.

Benjamin W L Margolis↗
NASA NTRSDate not supplied

Derivatives Across Adaptive-Step Integration Accurately and Efficiently

The numerical integration of ordinary differential equations (ODEs) is common in trajectory optimization. Previous studies have shown that the use of adaptive-step Runge-Kutta integration schemes can introduce errors in the derivatives due to non-differentiable behavior within the integration scheme itself. The authors previously demonstrated the use of an implicit adaptation to the Runge-Kutta methods to mitigate this issue, but at a significant computational cost. In this work, the authors demonstrate an explicit adaptation to the Runge-Kutta methods to address the issue that does not incur a significant computational cost.

Kaushik Ponnapalli↗
DOE OSTI2024

Systems Level Fuel Cycle Modeling in TMAP8 - A Demonstration

The tritium migration analysis program (TMAP) has been used for tritium inventory tracking and analysis for several years, and the Multiphysics Object Oriented Simulation Environment (MOOSE)-based TMAP8 has several improvements over TMAP4 and TMAP7, such as support for multiple dimensions and non-cartesian coordinate systems, as well as interoperability with sub-apps at higher and lower length scales. We demonstrate that TMAP8 has the additional capacity to solve systems-level problems using zero-dimensional ordinary differential equations by reproducing a literature model which describes a systems-level fuel-cycle of tritium inventory in a hypothetical fusion power plant. The capacity to run several coupled multi-scale physics calculations as part of a single package will be necessary for accurate blanket and fuel-cycle design.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

ChemComp: Compiling and Computing with Chemical Reaction Networks

The exponential growth in computing demands driven by scientific computing, data analytics, and artificial intelligence is pushing conventional CMOS-based high-performance computing systems to their physical and energy efficiency limits. As we approach the era of post-exascale computing, disruptive approaches are necessary to overcome these barriers and achieve substantial gains in energy efficiency. Analog and hybrid digital-analog computing systems have emerged as promising alternatives, offering the potential for orders-of-magnitude improvements in efficiency. Among these, biochemical computing stands out as a novel paradigm capable of leveraging the natural efficiency of chemical reactions, which have shown promise in solving optimization problems by converging to steady states. By scaling up reaction networks or reaction vessel sizes, biochemical systems present an opportunity to meet the high-performance demands of modern computing tasks. Despite their promise, significant theoretical and practical challenges remain, particularly in formulating and mapping computational problems to chemical reaction networks (CRNs) and designing viable biochemical computing devices. This paper addresses these challenges by introducing new ideas to ChemComp, a compilation and emulation framework for chemical computation. This work describes the mechanisms through which solutions to ordinary differential equations (ODEs) that can be represented as CRN systems can be achieved. Furthermore, we explain the design principles of an ODE dialect implemented as a multi-level intermediate representation (MLIR) compiler extension that will be coupled with existing infrastructure. We demonstrate the potential of our framework through a case study emulating a simplified chemical reservoir computing device. This work establishes foundational tools and methodologies necessary to harness the computational power of chemistry, paving the way for the development of energy-efficient, high-performance computing systems tailored to contemporary and future computational needs.

Bohm Agostini, Nicolas↗
DOE OSTI2025

Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.

Serrallés, José Cruz [Weill Cornell Med. Coll.]↗
DOE OSTI2021

TINES - Time Integration, Newton and Eigen Solver v. 1.0

SAND2021-1505 O. TINES is an open source software providing math infrastructure for solving many stiff time ordinary differential equations (ODEs) and/or differential algebraic equations (DAEs) using a batch hierarchical parallelism. The code is written using a parallel programming model (i.e., Kokkos) to future-proof the next generation parallel computing platforms such as GPU accelerators. This code is developed to support Exascale Catalytic Chemistry (ECC) Project. The code provides fundamental math helpers that can aid other research projects. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Kim, Kyungjoo↗
DOE OSTI2022

PolyODENet

Kinetics of a reaction network that follows mass-action rate laws can be described with a system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it is challenging to derive such kinetic differential equations from transient kinetic data without knowing the reaction network, especially when the data are incomplete due to experimental limitations. We introduce a program, PolyODENet, toward this goal. Based on the machine-learning method Neural ODE, PolyODENet defines a generative model and predicts concentrations at arbitrary time. As such, it is possible to include unmeasurable intermediate species in the kinetic equations. Importantly, we have implemented various measures to apply physical constraints and chemical knowledge in the training to regularize the solution space.

Wu, Qin [Brookhaven National Lab. (BNL), Upton, NY↗